Statistical geometry of particle packings. II. “Weak spots” in liquids

We investigate the statistical geometry of inherent structures (mechanically stable arrangements of particles generated by a steepest-descent mapping of equilibrium configurations to local potential minima) of liquid configurations of the shifted-force Lennard-Jones system, as an approach to elucidating mechanisms for the decay of metastable states. For a wide range of densities, including some higher than the triple point density, inherent structures are found to display remarkably heterogeneous geometry, with an apparently bicontinuous structure consisting of a compact phase and a void region. The void region is found to consist of a single system-spanning cavity. The volume fraction of this cavity vanishes above the density ${\rho }^{*}=\mathrm{0.89.}\mathrm{}$ This density coincides with the minimum in the pressure vs density curve for inherent structures, at negative pressure, indicating that the observed heterogeneity of the inherent structures is triggered by the crossing of a threshold of mechanical instability, much like the familiar spinodal concept. Analysis of spontaneous density fluctuations in the equilibrium and superheated liquid reveals that atoms present in regions of low density (weak spots) map predominantly to the cavity interface in the inherent structures. We discuss the relevance of these observations to limits of stability of the metastable liquid, nucleation, and, possibly, the glass transition.